Rather than a whole Pareto-optimal front, which demands too many points (especially in a high-dimensional space), the decision maker (DM) may only be interested in a partial region, called the region of interest (ROI). In this case, solutions outside this region can be noisy to the decision-making procedure. Even worse, there is no guarantee that we can find the preferred solutions when tackling problems with complicated properties or many objectives. In this paper, we develop a systematic way to incorporate the DM’s preference information into the decomposition-based evolutionary multiobjective optimization methods. Generally speaking, our basic idea is a nonuniform mapping scheme by which the originally evenly distributed reference points on a canonical simplex can be mapped to new positions close to the aspiration-level vector supplied by the DM. By this means, we are able to steer the search process toward the ROI either directly or interactively and also handle many objectives. Meanwhile, solutions lying on the boundary can be approximated as well given the DM’s requirements. Furthermore, the extent of the ROI is intuitively understandable and controllable in a closed form. Extensive experiments on a variety of benchmark problems with 2 to 10 objectives, fully demonstrate the effectiveness of our proposed method for approximating the preferred solutions in the ROI.

中文翻译：

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分解多目标优化中偏好的整合


决策者 (DM) 可能只对称为感兴趣区域 (ROI) 的部分区域感兴趣，而不是需要太多点（尤其是在高维空间中）的整个帕累托最优前沿。在这种情况下，该区域之外的解决方案可能会对决策过程产生干扰。更糟糕的是，当我们处理具有复杂性质或多个目标的问题时，并不能保证我们能够找到首选的解决方案。在本文中，我们开发了一种系统方法，将 DM 的偏好信息纳入基于分解的进化多目标优化方法。一般来说，我们的基本思想是一种非均匀映射方案，通过该方案，规范单纯形上最初均匀分布的参考点可以映射到接近 DM 提供的期望水平向量的新位置。通过这种方式，我们能够直接或交互地将搜索过程引导至投资回报率，并处理许多目标。同时，考虑到 DM 的要求，位于边界上的解也可以被近似。此外，投资回报率的范围以封闭的形式直观地可理解和可控。对具有 2 到 10 个目标的各种基准问题进行的广泛实验，充分证明了我们提出的方法在近似 ROI 中的首选解决方案方面的有效性。